How does a pile driving analyser measure force and velocity?

What sensors does a pile driving analyser use to collect data?

A pile driving analyser uses two types of sensors mounted directly on the pile: strain gauges and accelerometers. Strain gauges measure the deformation of the pile material as a stress wave passes through it during hammer impact. Accelerometers measure the acceleration of the pile at the same location. Both sensor types are typically installed in pairs on opposite sides of the pile to account for any bending effects.

The sensors are bolted or welded to the pile shaft, usually at a distance of one to two pile diameters below the pile head. This placement ensures that the measurements capture the stress wave before it is disturbed by reflections from the pile head or the hammer assembly. The data acquisition unit records both signals simultaneously at a high sampling rate, producing time-history records of strain and acceleration throughout each hammer blow.

For the measurements to be reliable, the sensors must be properly calibrated, and the pile cross-section at the sensor location must be well defined. This is straightforward for steel piles with a constant, known cross-section, but becomes more complex for cast-in-situ concrete piles, where the cross-sectional area and material stiffness can vary along the pile length.

How is force calculated from strain measurements in a pile?

Force at the pile head is calculated by multiplying the measured strain by the pile’s axial stiffness, which is the product of the pile’s cross-sectional area and the elastic modulus of the pile material. The formula is: Force = Strain × Area × Elastic Modulus. This relationship assumes the pile behaves as a linear elastic rod during the brief duration of the hammer impact.

In practice, this means the accuracy of the force calculation depends directly on how well the pile’s material properties and geometry are known. For steel piles with a constant cross-section, the elastic modulus and area are well defined, and the force calculation is reliable. For concrete piles, particularly cast-in-situ types, both the cross-sectional area and the concrete stiffness can vary along the pile length and are not always clearly defined at the time of testing. This introduces additional uncertainty into the derived force values.

Using two strain gauges on opposite sides of the pile and averaging their readings helps reduce the influence of any bending in the pile during driving. The averaged strain value is then used in the force calculation, producing a more representative result than a single gauge would provide.

How is velocity derived from accelerometer readings during pile driving?

Velocity at the pile head is derived by numerically integrating the acceleration signal over time. Since the accelerometers record how quickly the pile is accelerating at each instant during the hammer blow, integrating that signal once with respect to time gives the velocity of the pile at the measurement point. A second integration of the velocity signal gives displacement.

This integration process introduces a potential source of inaccuracy. Any baseline drift or noise in the raw acceleration signal accumulates during integration, which can shift the resulting velocity and displacement values. Careful signal conditioning and the use of well-maintained, high-quality accelerometers help minimise this effect. For steel piles, the resulting velocity signal is generally reliable. For cast-in-situ concrete piles, where the pile’s response to the hammer impact is less predictable, the integrated velocity and displacement values carry greater uncertainty.

The velocity signal is recorded at the same location and at the same time as the strain signal, so force and velocity are always synchronised. This synchronisation is what makes the subsequent wave equation analysis possible.

What is the relationship between force and velocity in stress wave analysis?

In stress wave analysis, force and velocity at the pile head are directly related through the pile’s impedance, which is the product of the pile’s cross-sectional area and elastic modulus divided by the wave speed. For a pile with no soil resistance and no reflections, force equals impedance multiplied by velocity. Deviations from this relationship reveal the presence of soil resistance, changes in pile cross-section, or structural defects.

When a hammer strikes the pile, a compressive stress wave travels downward through the pile. As this wave encounters changes in impedance, whether from soil resistance along the shaft, a change in pile cross-section, or the pile toe, part of the wave reflects back upward toward the pile head. The pattern of these reflections, captured in the force and velocity time histories, contains information about the pile’s structural condition and the distribution of soil resistance along its length.

Signal matching analysis uses this relationship systematically. A soil model is constructed, and the calculated force response is compared with the measured response. The model parameters are adjusted iteratively until the calculated and measured signals align. At that point, the calibrated model provides an estimate of the mobilised static bearing capacity and the distribution of soil resistance. Software such as AllWave-DLT supports this analysis process, allowing experienced engineers to extract reliable capacity estimates from the raw force and velocity data.

What factors can affect the accuracy of PDA force and velocity measurements?

Several factors influence how accurately a pile driving analyser captures force and velocity. The most important are pile geometry, material properties, sensor quality, and the consistency of the hammer impact. When any of these factors introduce uncertainty, the reliability of the derived measurements and the subsequent analysis decreases.

Pile type and geometry

Steel piles with a constant cross-section and known material properties provide the most favourable conditions for accurate measurement. The force calculation relies on a well-defined area and elastic modulus, both of which are stable and predictable for steel. Cast-in-situ concrete piles present the opposite situation: the cross-sectional area may vary along the pile length, and the concrete stiffness depends on mix quality, curing conditions, and age. These variables make both the force and velocity derivations less precise, and the resulting analysis carries a wider bandwidth of possible outcomes.

Soil conditions and pile configuration

End-bearing piles with a long free-standing length and their toe in rock or dense granular soil produce cleaner stress wave signals that are easier to interpret. Friction piles with minimal free-standing length generate more complex reflection patterns, making signal matching more challenging. In cohesive soils such as clay, the fast nature of the dynamic test means that time-dependent behaviour and pore water pressure effects are not captured, which limits what the measurements can tell you about long-term pile performance. Significant soil resistance from cohesive layers reduces the accuracy of capacity estimates derived from PDA data.

Equipment and field practice

Well-maintained, properly calibrated sensors and a reliable data acquisition unit are a baseline requirement for accurate measurements. Sensors that are poorly attached, damaged, or out of calibration introduce errors that no amount of post-processing can correct. The drop mass used to generate the hammer impact also matters: its weight and drop height must deliver enough energy to fully mobilise soil resistance, and the shape of the drop mass influences the peak stresses generated in the pile during the blow.

How does PDA data feed into pile capacity and integrity assessment?

PDA data feeds into pile capacity and integrity assessment through signal matching analysis, a wave equation-based process in which a soil and pile model is calibrated against the measured force and velocity records. Once the model reproduces the measured response, it provides estimates of mobilised static bearing capacity, the distribution of soil resistance along the pile shaft and at the toe, and any structural anomalies in the pile.

The integrity assessment works by examining the force and velocity signals for unexpected reflections. A reflection arriving earlier than expected from the pile toe indicates a change in impedance above the toe, which may signal a crack, a reduction in cross-section, or a construction defect. The timing and magnitude of the reflection help locate and characterise the anomaly.

For capacity assessment, the quality of the result depends heavily on the engineer performing the signal matching. Because a signal matching model contains many parameters, different parameter combinations can produce equally plausible fits to the measured data. This user dependency means that results from the same pile can vary between analysts. Conditions that produce the smallest bandwidth of outcomes, and therefore the most reliable capacity estimates, include:

End-bearing steel piles with a constant cross-section and a long free-standing length
Pile toe in rock or dense granular soil
Testing performed at restrike after sufficient setup time has elapsed
Signal matching carried out by a qualified, experienced engineer using suitable software
Field measurements collected with well-maintained, properly calibrated equipment

It is worth noting that signal matching always produces more reliable results than simplified direct methods such as the CASE method or driving formulae applied directly to field data, even when conditions are not ideal. The CASE method and driving formulae use simplified assumptions that cannot account for the complexity of real pile-soil interaction, whereas signal matching builds a full model of that interaction from the measured data.

Where dynamic testing alone cannot provide sufficient certainty, for example with friction piles in cohesive soils or large-diameter bored concrete piles, pile load testing for direct capacity measurement using static or rapid methods provides a direct measurement of load-settlement behaviour that PDA analysis cannot replicate.

How Allnamics Supports PDA Measurement and Analysis

We combine in-house developed hardware, advanced software, and decades of signal matching expertise to deliver reliable dynamic load testing results across a wide range of pile types and project conditions. Our approach covers every stage of the process, from sensor installation and data acquisition to post-processing and engineering interpretation.

PDR data acquisition system: Our proprietary PDR unit captures high-quality strain and acceleration data during pile driving, providing the accurate raw measurements that signal matching depends on.
AllWave-DLT software: We use our own signal matching software to analyse force and velocity records, producing calibrated soil models and capacity estimates that your team can rely on for design decisions.
Experienced engineering interpretation: Our engineers have decades of hands-on experience with signal matching across steel piles, concrete piles, onshore projects, and offshore programs. We understand where the method is reliable and where its limitations require supplementary testing.
Integrated testing programs: We combine dynamic load testing with static load testing or Rapid Load Testing where project conditions call for a higher level of certainty, particularly for friction piles or piles in cohesive soils.
Onshore and offshore capability: We perform PDA measurements and analysis on projects worldwide, including large-scale offshore wind foundation programs where testing efficiency and data quality are both critical.

If your project involves driven piles and you want accurate, independently interpreted dynamic load testing results, contact us to discuss your testing program and how we can support your foundation verification objectives.